Signal processing is used in virtually every type of electronic device ranging from satellite communication systems to digital cameras. Many of the signals processed are nonlinear with various peaks and valleys in the signal. For processing a signal every single point on the nonlinear curve should be known. However, this involves a tremendous number of parameters to locate every point. Thus, a nonlinear optimization process is used to approximate the nonlinear curve. Unfortunately, this still involves a large number of parameters. On one hand, this increases the computation complexity involved in the approximation and, on the other hand, it increases the possibility that the optimization process will be trapped into one of the local minima, or valleys, of the nonlinear curve.
To date, an enormous amount of research has been performed in an attempt to develop multiple-variable optimization methods to avoid local minima and directly locate the global minimum or lowest valley for the entire non-linear curve without developing a simple system.
In another approach, the number of parameters is reduced through a simplification of the nonlinear objective function. The simplest way to approximate the nonlinear curve is to use piecewise linear functions. However, unless the curves being approximated are also piecewise linear, a large number of endpoint coordinates for the linear functions must be created to achieve reasonable accuracy.
Thus, a need still remains for nonlinear optimization in signal processing. In view of the increasing use of signal processing, it is becoming increasingly critical that answers be found to these problems.
Solutions to these problems have been long sought but prior developments have not taught or suggested any solutions and, thus, solutions to these problems have long eluded those skilled in the art.